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Approximations and Randomization to Boost CSP Techniques
 Annals of Operations Research
, 2004
"... Abstract. In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for sol ..."
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Abstract. In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly difficult to successfully integrate LPbased and CSPbased methods in a purely combinatorial setting. Our approach draws on recent results on approximation algorithms based on LP relaxations and randomized rounding techniques, with theoretical guarantees, as well on results that provide evidence that the runtime distributions of combinatorial search methods are often heavytailed. We propose a complete randomized backtrack search method for combinatorial problems that tightly couples CSP propagation techniques with randomized LPbased approximations. We present experimental results that show that our hybrid CSP/LP backtrack search method outperforms the pure CSP and pure LP strategies on instances of a hard combinatorial problem. 1.
Solving MAXSAT and Weighted MAXSAT Problems Using BranchandCut
, 1998
"... We describe a branch and cut algorithm for both MAXSAT and weighted MAXSAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. W ..."
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We describe a branch and cut algorithm for both MAXSAT and weighted MAXSAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm and a SemiDefinite Programming (SDP) approach. Our algorithm is more effective than EDPL on some problems, notably MAX2SAT. EDPL and SDP are more effective on some other classes of problems.
C.: Quality of LPbased approximations for highly combinatorial problems
 In: International Conference on Principles and Practice of Constraint Programming (CP
, 2004
"... Abstract. We study the quality of LPbased approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in t ..."
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Abstract. We study the quality of LPbased approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in the solution integrality of the relaxation. The solution quality of approximation schemes degrades substantially near phase transition boundaries. Our findings are consistent over a range of LPbased approximation schemes. We also provide results on the extent to which LP relaxations can provide a global perspective of the search space and therefore be used as a heuristic to guide a complete solver.
A Hybrid Genetic Algorithm for the Satisfiability Problem
"... This paper introduces a hybrid genetic algorithm for the satisfiability problem (SAT). This algorithm, called GASAT, incorporates local search within the genetic framework. GASAT relays on a problem specific crossover operator to create new solutions, that are improved by a tabu search procedure. Th ..."
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This paper introduces a hybrid genetic algorithm for the satisfiability problem (SAT). This algorithm, called GASAT, incorporates local search within the genetic framework. GASAT relays on a problem specific crossover operator to create new solutions, that are improved by a tabu search procedure. The performance of GASAT is assessed using a set of wellknown benchmarks. Comparisons with stateoftheart SAT algorithms show that GASAT gives competitive results.
Protein interaction inference as a maxsat problem
 Proc. of IEEE CVPR 2005 Workshop on Computer Vision Methods for Bioinformatics, 2005. Proceedings of the Sixth International Conference on Data Mining (ICDM'06) 0769527019/06 $20.00 © 2006
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Proceedings CPAIOR’02 The Promise of LP to Boost CSP Techniques for Combinatorial Problems
"... In recent years we have seen an increasing interest in combining CSP and LP based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, ..."
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In recent years we have seen an increasing interest in combining CSP and LP based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly difficult to successfully integrate LPbased and CSPbased methods in a purely combinatorial setting. We propose a complete randomized backtrack search method for combinatorial problems that tightly couples CSP propagation techniques with randomized LP rounding. Our approach draws on recent results on approximation algorithms with theoretical guarantees, based on LP relaxations and randomized rounding techniques, as well on results that provide evidence that the run time distributions of combinatorial search methods are often heavytailed. We present experimental results that show that our hybrid CSP/LP backtrack search method outperforms the pure CSP and pure LP strategies on instances of a hard combinatorial problem. 1
LP as a Global Search Heuristic Across Different Constrainedness Regions ⋆ Extended Abstract
"... Abstract. We study the behavior of heuristics based on the LP relaxation with respect to the underlying constraindness of the problem. Our study focuses on the Latin square (or quasigroup) completion problem [1]) 1 as a prototype for highly combinatorial problems. We find that simple techniques base ..."
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Abstract. We study the behavior of heuristics based on the LP relaxation with respect to the underlying constraindness of the problem. Our study focuses on the Latin square (or quasigroup) completion problem [1]) 1 as a prototype for highly combinatorial problems. We find that simple techniques based on the LP relaxation of the problem provide satisfactory guidance for under and overconstrained instances. In the critically constrained region, the performance of such simple techniques degrades, due to the inherit hardness of the problem. In this setting, we examine a technique that recomputes the LP relaxation every time a variable is set. This leads to a significant increase in performance, suggesting that carefully designed “one step at a time ” LPbased heuristics could provide suitable guidance even for the hardest instances. Recent years have witnessed the emergence of a new area involving hybrid solvers integrating CP and ORbased methods. OR has a long and rich history of using Linear Programming (LP) based relaxations for (Mixed) Integer
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"... These experiments have also shown that, in general, both same rise–fall and greedy approaches obtain results very close to the optimum, at least for the library used. This happens despite the fact that the library contained gates with significantly different rise and fall delays. We believe this is ..."
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These experiments have also shown that, in general, both same rise–fall and greedy approaches obtain results very close to the optimum, at least for the library used. This happens despite the fact that the library contained gates with significantly different rise and fall delays. We believe this is due to the fact that even for circuits with a moderate number of levels (say 5), the imbalances in the individual rise and fall gate delays cancel out by the time the primary outputs are reached. Nevertheless, we were able to show for the first time that for the loadindependent delay model in the presence of rise and fall delays, same rise–fall and greedy approaches work quite well, achieving exact results on 43 and 57 circuits, respectively, out of 73. There are several interesting directions for future work. One obvious direction for future research is the search for an exact pseudopolynomial algorithm for general combinational circuits. Another interesting area of research is the application of this method to the technology
(0,±1) Ideal Matrices
 Mathematical Programming, Series A
, 1996
"... A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of finding a satisfactory characterization of those matrices which are minimally nonideal is a well known open problem. An outstanding result toward the solution of this pr ..."
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A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of finding a satisfactory characterization of those matrices which are minimally nonideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally nonideal matrices. In this paper we consider the extension of the notion of ideality to (0; \Sigma1) matrices. By means of a standard transformation, we associate with any (0; \Sigma1) matrix A a suitable (0; 1) matrix D(A). Then we introduce the concept of disjoint completion A + of a (0; \Sigma1) matrix A and we show that A is ideal if and only if D(A + ) is ideal. Moreover, we introduce a suitable concept of a minimally nonideal (0; \Sigma1) matrix and we prove a Lehmantype characterization of minimally nonideal (0; \Sigma1) matrices. 1 Introduction Let A be a (0; \Sigma1) matrix whose sets of ...